The graph shown in the image is of a V-shaped function, likely representing an absolute value function. The vertex of the graph is at the point $(0, -2)$, and the arms of the graph open upwards.

Domain and Range Analysis:

• Domain: The domain represents all possible $x$-values that the function can take. From the graph, we see that the function extends infinitely in both directions horizontally, which means the domain is all real numbers: $\text{Domain} = (-\infty, \infty) \quad \text{or} \quad \text{all real numbers}.$

• Range: The range represents all possible $y$-values that the function outputs. The lowest point on the graph is $y = -2$, and the graph increases from there as $x$ moves in either direction. Therefore, the range is $y \geq -2$: $\text{Range} = [-2, \infty).$

Thus, the answers provided in the image, stating the domain as all real numbers and the range as $y \geq -2$, are correct.

Would you like further details or explanations?

Here are 5 follow-up questions based on this explanation:

1. How do you find the domain of different types of functions?
2. Can an absolute value function have a different vertex than $(0, -2)$?
3. What are the general properties of an absolute value function?
4. How do you determine the range of a function graphically?
5. How does the slope of the arms in an absolute value function affect the graph?

Tip: Always check the vertex of an absolute value function to determine its minimum or maximum, which helps in defining the range.